MinT - Best Known (144, 144+43, s)-Nets in Base 2

Best Known (144, 144+43, s)-Nets in Base 2

(144, 144+43, 195)-Net over F₂ — Constructive and digital

Digital (144, 187, 195)-net over F₂, using

8 times m-reduction [i] based on digital (144, 195, 195)-net over F₂, using
- trace code for nets [i] based on digital (14, 65, 65)-net over F₈, using
  - net from sequence [i] based on digital (14, 64)-sequence over F₈, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈ with g(F) = 14 and N(F) ≥ 65, using
      - the Suzuki function field over F₈ [i]

(144, 144+43, 329)-Net over F₂ — Digital

Digital (144, 187, 329)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(144, 144+43, 3994)-Net in Base 2 — Upper bound on s

There is no (144, 187, 3995)-net in base 2, because

1 times m-reduction [i] would yield (144, 186, 3995)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 98 573398 232975 262717 861542 241522 549664 072185 608561 217472 > 2¹⁸⁶ [i]